##f(x,y)##(adsbygoogle = window.adsbygoogle || []).push({});

a critical point is given by ##f_x=0## and ##f_y=0## simultaneously.

the test is:

##D=f_{xx}f_{yy}-(f_{xy})^2 ##

if ##D >0 ## and ##f_{xx} <0 ## it is a max

if ##D >0 ## and ##f_{xx} >0 ## it is a min

##D >0 ## is is a saddle

if ##D =0 ## it is inconclusive, and ##f_x## and ##f_y## are not linear independent.

I'm stuck on the ##D=0## comment re linear independence. So is this saying that ##x## and ##y## are not linear indepedent?

So if i take an arbitary function ##f(x,y) ## and ##y=h(x)##, h some linear function, then I should get ##D=0## or not?

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# I Function of 2 variables, max/min test, D=0 and linear dependence

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